An unknown alcohol is treated with the 'Lucas reagent' to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism?

The reaction of alcohol with Lucas reagent is mostly SN1 reaction and the rate of reaction is directly proportional to the stability of carbocation formed in the reaction.Since 3o R–OH forms 3o carbocation (most stable) hence it will react fastest by SN1 reaction.